Embeddings and labeling schemes for A*

TL;DR

This paper explores learned heuristic functions for A* graph search, focusing on embeddings and labeling schemes, providing theoretical bounds and demonstrating near-optimal tradeoffs between representation complexity and search efficiency.

Contribution

It formalizes feature-based heuristics for A*, analyzes bounds for embeddings and labeling schemes, and shows these bounds are nearly optimal under natural assumptions.

Findings

Lower bounds established for embedding dimensions and label bits versus A* running time.

Tradeoff analysis between representation complexity and search efficiency.

Bounds are nearly optimal under natural assumptions.

Abstract

A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics have been handcrafted by domain experts. However, over the last few years, there has been a growing interest in learning heuristic functions. Such learned heuristics estimate the distance between given nodes based on "features" of those nodes. In this paper we formalize and initiate the study of such feature-based heuristics. In particular, we consider heuristics induced by norm embeddings and distance labeling schemes, and provide lower bounds for the tradeoffs between the number of dimensions or bits used to represent each graph node, and the running time of the A* algorithm. We also show that, under natural assumptions, our lower bounds are almost optimal.